arXiv:2607. 13042v1 Announce Type: new Abstract: This paper traces, with explicit numerical values, how PyTorch's automatic differentiation (AD) engine computes gradients for Physics-Informed Neural Network (PINN) training -- a setting that requires two levels of differentiation: computing the physics derivative $\hat{y}'(t)=d\hat{y}/dt$ through the network, and computing parameter gradients $\nabla_\theta L$ of a loss that itself depends on $\hat{y}'(t)$.
By Abdeladhim Tahimi
arXiv:2606. 16926v1 Announce Type: cross Abstract: Functional optimization problems are typically solved by optimizing the parameters of a fixed representation, such as a neural network, resulting in highly nonconvex losses that complicate both training and theoretical analysis.
By Daniel Csillag, Rodrigo Schuller, Pedro Dall'Antonia, Leonidas Guibas, Luiz Velho, Tiago Novello
arXiv:2609.15355v1 Announce Type: cross
Abstract: We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by deep ReLU neural network...
By Shuhao Jiao
arXiv:2604. 07328v3 Announce Type: replace Abstract: How does the choice of training data influence an AI model?
By Sam Gunn
arXiv:2609.15355v2 Announce Type: replace-cross
Abstract: We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by ReLU neural netw...
By Shuhao Jiao
We systematically investigate finite-difference (FD) derivative computation in Physics-Informed Neural Networks (PINNs) as an alternative to automatic differentiation (AD). On three benchmark PDEs we show that, with a properly calibrated step size, FD matches AD in accuracy on every problem while running faster across the full tested batch-size range and using substantially less GPU memory, and that a stochastic variant we propose outperforms AD on a stationary problem.